Multiscale search using probabilistic quadtrees

Abstract — We propose a novel framework to search for a static target using a multiscale representation. The algorithm we present is appropriate when the target detection sensor trades off accuracy versus covered area, e.g., when a UAV can fly and sense at different elevations. A structure based on quadtrees is used to propagate a posterior about the target location using a variable resolution representation that is dynamically refined in regions associated with higher probability of target presence. Probabilities are updated using a Bayesian approach accounting for erroneous sensor readings in the form of false positives and missed detections. The model we propose is coupled with a search and decision algorithm that determines where to sense next and with which accuracy. The search algorithm is based on an objective function accounting for both probability of detection and motion costs, thus aiming to minimize traveled distances while trying to localize the target. The paper is concluded with simulation results showing our approach outperforms commonly used methods based on uniform resolution grids. I

Multi-level mapping: Real-time dense monocular SLAM

We present a method for Simultaneous Localization and Mapping (SLAM) using a monocular camera that is capable of reconstructing dense 3D geometry online without the aid of a graphics processing unit (GPU). Our key contribution is a multi-resolution depth estimation and spatial smoothing process that exploits the correlation between low-texture image regions and simple planar structure to adaptively scale the complexity of the generated keyframe depthmaps to the texture of the input imagery. High-texture image regions are represented at higher resolutions to capture fine detail, while low-texture regions are represented at coarser resolutions for smooth surfaces. The computational savings enabled by this approach allow for significantly increased reconstruction density and quality when compared to the state-of-the-art. The increased depthmap density also improves tracking performance as more constraints can contribute to the pose estimation. A video of experimental results is available at http://groups.csail.mit.edu/rrg/multi_level_mapping.Charles Stark Draper Laboratory (Research Fellowship

Probabilistic and Deep Learning Algorithms for the Analysis of Imagery Data

Accurate object classification is a challenging problem for various low to high resolution imagery data. This applies to both natural as well as synthetic image datasets. However, each object recognition dataset poses its own distinct set of domain-specific problems. In order to address these issues, we need to devise intelligent learning algorithms which require a deep understanding and careful analysis of the feature space. In this thesis, we introduce three new learning frameworks for the analysis of both airborne images (NAIP dataset) and handwritten digit datasets without and with noise (MNIST and n-MNIST respectively). First, we propose a probabilistic framework for the analysis of the NAIP dataset which includes (1) an unsupervised segmentation module based on the Statistical Region Merging algorithm, (2) a feature extraction module that extracts a set of standard hand-crafted texture features from the images, (3) a supervised classification algorithm based on Feedforward Backpropagation Neural Networks, and (4) a structured prediction framework using Conditional Random Fields that integrates the results of the segmentation and classification modules into a single composite model to generate the final class labels. Next, we introduce two new datasets SAT-4 and SAT-6 sampled from the NAIP imagery and use them to evaluate a multitude of Deep Learning algorithms including Deep Belief Networks (DBN), Convolutional Neural Networks (CNN) and Stacked Autoencoders (SAE) for generating class labels. Finally, we propose a learning framework by integrating hand-crafted texture features with a DBN. A DBN uses an unsupervised pre-training phase to perform initialization of the parameters of a Feedforward Backpropagation Neural Network to a global error basin which can then be improved using a round of supervised fine-tuning using Feedforward Backpropagation Neural Networks. These networks can subsequently be used for classification. In the following discussion, we show that the integration of hand-crafted features with DBN shows significant improvement in performance as compared to traditional DBN models which take raw image pixels as input. We also investigate why this integration proves to be particularly useful for aerial datasets using a statistical analysis based on Distribution Separability Criterion. Then we introduce a new dataset called noisy-MNIST (n-MNIST) by adding (1) additive white gaussian noise (AWGN), (2) motion blur and (3) Reduced contrast and AWGN to the MNIST dataset and present a learning algorithm by combining probabilistic quadtrees and Deep Belief Networks. This dynamic integration of the Deep Belief Network with the probabilistic quadtrees provide significant improvement over traditional DBN models on both the MNIST and the n-MNIST datasets. Finally, we extend our experiments on aerial imagery to the class of general texture images and present a theoretical analysis of Deep Neural Networks applied to texture classification. We derive the size of the feature space of textural features and also derive the Vapnik-Chervonenkis dimension of certain classes of Neural Networks. We also derive some useful results on intrinsic dimension and relative contrast of texture datasets and use these to highlight the differences between texture datasets and general object recognition datasets

Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

In robotics, Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent the spatial topologies of their surrounding area. In this paper we consider the problem of constructing GVDs on discrete environments. Several algorithms that solve this problem exist in the literature, notably the Brushfire algorithm and its improved versions which possess local repair mechanism. However, when the area to be processed is very large or is of high resolution, the size of the metric matrices used by these algorithms to compute GVDs can be prohibitive. To address this issue, we propose an improvement on the current algorithms, using pointerless quadtrees in place of metric matrices to compute and maintain GVDs. Beyond the construction and reconstruction of a GVD, our algorithm further provides a method to approximate roadmaps in multiple granularities from the quadtree based GVD. Simulation tests in representative scenarios demonstrate that, compared with the current algorithms, our algorithm generally makes an order of magnitude improvement regarding memory cost when the area is larger than 210×210. We also demonstrate the usefulness of the approximated roadmaps for coarse-to-fine pathfinding tasks

A Multiscale Guide to Brownian Motion

We revise the Levy's construction of Brownian motion as a simple though still rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based "geometrical features" at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for fractional Brownian motion, Ornstein-Uhlenbeck process, Gaussian free field, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Sum-Product Graphical Models: a Graphical Model Perspective on Sum-Product Networks

The trade off between expressiveness of representation and tractability of inference is a key issue of probabilistic models. On the one hand, probabilistic Graphical Models (GMs) provide a high level representation of distributions, but exact inference with cyclic graphs is in general intractable. On the other hand, Sum-Product Networks (SPNs) allow tractable exact inference with probability distributions that are more complex than tractable GMs, but they employ a low level representation of the underlying distribution, which is much harder to read and interpret than in GMs. The objective of this thesis is to close this gap and to achieve simultaneously the high level representation of GMs and the efficiency of SPNs. To this aim, new models and procedures are introduced. We first investigate SPNs that include GMs as a submodule, obtaining a derivation of Expectation-Maximization for SPNs which is the first allowing to learn the GM part alongside the SPN parameters. Then, we introduce a new architecture called Sum-Product Graphical Model (SPGM). This new architecture is the first to combine the semantics of graphical models with the evaluation efficiency of SPNs: SPGMs always enable tractable inference using a class of models that incorporate context specific independence (like SPNs), and they provide a high-level model interpretation in terms of conditional independence assumptions and corresponding factorizations (like GMs). An algorithm for learning both the structure and the model parameters of SPGMs is also introduced. Finally, several applications that illustrate and empirically motivate the introduction of the new models are described. SPGMs are applied to real-world discrete density estimation datasets, to augment a graphical model for segmenting scans of the human retina and detecting local pathologies, and to model very large mixtures of Quadtrees for image denoising. Strong empirical results and novel application areas denote promise for future applications of SPGMs

Efficient mobile robot path planning by Voronoi-based heuristic

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A distributed Quadtree Dictionary approach to multi-resolution visualization of scattered neutron data

Grid computing is described as dependable, seamless, pervasive access to resources and services, whereas mobile computing allows the movement of people from place to place while staying connected to resources at each location. Mobile grid computing is a new computing paradigm, which joins these two technologies by enabling access to the collection of resources within a user\u27s virtual organization while still maintaining the freedom of mobile computing through a service paradigm. A major problem in virtual organization is needs mismatch, in which one resources requests a service from another resources it is unable to fulfill, since virtual organizations are necessarily heterogeneous collections of resources. In this dissertation we propose a solution to the needs mismatch problem in the case of high energy physics data. Specifically, we propose a Quadtree Dictionary (QTD) algorithm to provide lossless, multi-resolution compression of datasets and enable their visualization on devices of all capabilities. As a prototype application, we extend the Integrated Spectral Analysis Workbench (ISAW) developed at the Intense Pulsed Neutron Source Division of the Argonne National Laboratory into a mobile Grid application, Mobile ISAW. In this dissertation we compare our QTD algorithm with several existing compression techniques on ISAW\u27s Single-Crystal Diffractometer (SCD) datasets. We then extend our QTD algorithm to a distributed setting and examine its effectiveness on the next generation of SCD datasets. In both a serial and distributed setting, our QTD algorithm performs no worse than existing techniques such as the square wavelet transform in terms of energy conservation, while providing the worst-case savings of 8:1

Automatic near real-time flood detection in high resolution X-band synthetic aperture radar satellite data using context-based classification on irregular graphs

This thesis is an outcome of the project “Flood and damage assessment using very high resolution SAR data” (SAR-HQ), which is embedded in the interdisciplinary oriented RIMAX (Risk Management of Extreme Flood Events) programme, funded by the Federal Ministry of Education and Research (BMBF). It comprises the results of three scientific papers on automatic near real-time flood detection in high resolution X-band synthetic aperture radar (SAR) satellite data for operational rapid mapping activities in terms of disaster and crisis-management support. Flood situations seem to become more frequent and destructive in many regions of the world. A rising awareness of the availability of satellite based cartographic information has led to an increase in requests to corresponding mapping services to support civil-protection and relief organizations with disaster-related mapping and analysis activities. Due to the rising number of satellite systems with high revisit frequencies, a strengthened pool of SAR data is available during operational flood mapping activities. This offers the possibility to observe the whole extent of even large-scale flood events and their spatio-temporal evolution, but also calls for computationally efficient and automatic flood detection methods, which should drastically reduce the user input required by an active image interpreter. This thesis provides solutions for the near real-time derivation of detailed flood parameters such as flood extent, flood-related backscatter changes as well as flood classification probabilities from the new generation of high resolution X-band SAR satellite imagery in a completely unsupervised way. These data are, in comparison to images from conventional medium-resolution SAR sensors, characterized by an increased intra-class and decreased inter-class variability due to the reduced mixed pixel phenomenon. This problem is addressed by utilizing multi-contextual models on irregular hierarchical graphs, which consider that semantic image information is less represented in single pixels but in homogeneous image objects and their mutual relation. A hybrid Markov random field (MRF) model is developed, which integrates scale-dependent as well as spatio-temporal contextual information into the classification process by combining hierarchical causal Markov image modeling on automatically generated irregular hierarchical graphs with noncausal Markov modeling related to planar MRFs. This model is initialized in an unsupervised manner by an automatic tile-based thresholding approach, which solves the flood detection problem in large-size SAR data with small a priori class probabilities by statistical parameterization of local bi-modal class-conditional density functions in a time efficient manner. Experiments performed on TerraSAR-X StripMap data of Southwest England and ScanSAR data of north-eastern Namibia during large-scale flooding show the effectiveness of the proposed methods in terms of classification accuracy, computational performance, and transferability. It is further demonstrated that hierarchical causal Markov models such as hierarchical maximum a posteriori (HMAP) and hierarchical marginal posterior mode (HMPM) estimation can be effectively used for modeling the inter-spatial context of X-band SAR data in terms of flood and change detection purposes. Although the HMPM estimator is computationally more demanding than the HMAP estimator, it is found to be more suitable in terms of classification accuracy. Further, it offers the possibility to compute marginal posterior entropy-based confidence maps, which are used for the generation of flood possibility maps that express that the uncertainty in labeling of each image element. The supplementary integration of intra-spatial and, optionally, temporal contextual information into the Markov model results in a reduction of classification errors. It is observed that the application of the hybrid multi-contextual Markov model on irregular graphs is able to enhance classification results in comparison to modeling on regular structures of quadtrees, which is the hierarchical representation of images usually used in MRF-based image analysis. X-band SAR systems are generally not suited for detecting flooding under dense vegetation canopies such as forests due to the low capability of the X-band signal to penetrate into media. Within this thesis a method is proposed for the automatic derivation of flood areas beneath shrubs and grasses from TerraSAR-X data. Furthermore, an approach is developed, which combines high resolution topographic information with multi-scale image segmentation to enhance the mapping accuracy in areas consisting of flooded vegetation and anthropogenic objects as well as to remove non-water look-alike areas